A224138 Number of 7 X n 0..1 arrays with rows nondecreasing and antidiagonals unimodal.

128, 2187, 9688, 25047, 52581, 101412, 186348, 329167, 561329, 927323, 1488515, 2327716, 3554534, 5311574, 7781550, 11195373, 15841279, 22075061, 30331469, 41136842, 55123036, 73042712, 95786048, 124398939, 160102749, 204315679

Offset

1,1

Comments

Row 7 of A224133.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = (4/315)*n^7 + (1/5)*n^6 + (112/45)*n^5 + (461/24)*n^4 + (19267/180)*n^3 + (50171/120)*n^2 + (463243/420)*n - 511 for n>5.

Conjectures from Colin Barker, Aug 27 2018: (Start)

G.f.: x*(128 + 1163*x - 4224*x^2 + 1611*x^3 + 9957*x^4 - 14526*x^5 + 3960*x^6 + 4357*x^7 - 1401*x^8 - 1818*x^9 + 659*x^10 + 353*x^11 - 155*x^12) / (1 - x)^8.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>13.

(End)

Example

Some solutions for n=3:
..0..0..1....1..1..1....0..1..1....0..0..0....1..1..1....0..0..0....0..1..1
..0..1..1....0..0..1....1..1..1....1..1..1....1..1..1....0..0..0....0..0..1
..0..0..1....0..0..1....1..1..1....1..1..1....0..0..1....0..1..1....0..1..1
..0..0..0....0..0..1....0..0..0....0..1..1....0..0..0....1..1..1....0..0..0
..0..1..1....0..0..1....0..1..1....0..0..0....0..0..0....0..0..1....0..1..1
..0..0..0....0..1..1....0..0..1....0..0..1....0..0..0....0..1..1....0..0..0
..0..0..1....0..0..1....0..0..0....0..0..0....1..1..1....0..0..0....0..0..0

Crossrefs

Cf. A224133.

Sequence in context: A321831 A351195 A223954 * A331198 A250365 A017678

Adjacent sequences: A224135 A224136 A224137 * A224139 A224140 A224141

Keyword

nonn

Author

R. H. Hardin, Mar 31 2013

Status

approved